THE INFLUENCE OF PICK-UP IONS ON SPACE PLASMA DISTRIBUTIONS

The addition and incorporation of highly ordered distributions of pickup ions can increase the ordering of space plasmas, decreasing their entropy, and driving them away from equilibrium. In this study, we present a model for describing the entropy decrease of heliospheric plasmas caused by the pick-up ions and their highly ordered arrangement. We consider a plasma flow consisting of two proton populations: (1) a solar wind distribution that is in quasi-equilibrium and ( 2) a spherical shell distribution of pick-up protons. Because all protons are indistinguishable, they equally share a hybrid state, where the hybrid probability distribution is given by the normalized sum of the distributions of the solar wind and pick-up protons. We derive an analytical formulation of the thickness of the pick-up proton shell distribution. Then we show that the entropy of the hybrid state depends on a dimensionless fluctuation number, Theta, which is a measure of the organizing role of pick-up protons. This number characterizes and compares two types of fluctuations, the thermal motion of solar wind protons and the bounded motion of pick-up protons that forms the spherical shell distribution. We find that the entropy variation between the hybrid and original states is proportional to the negative logarithm of Theta. When the two competing fluctuations balance each other, Theta similar to 1, the pick-up protons have no effect on the entropy of solar wind protons. Remarkably, while sunward of the termination shock pick-up ions act to slightly increase entropy, throughout the inner heliosheath their effect is to decrease the entropy dramatically.